Use the graph below to answer the following question:
What is the average rate of change from x = –4 to x = 1?
–3
–1
0
1
Answers
average rate of change = (-1 - 4) / 1 - (-4) = -5 / 5 = -1
The average rate of change from x = –4 to x = 1 is 3.
Explanation:To find the average rate of change from x = –4 to x = 1, we need to calculate the change in y-values and divide it by the change in x-values. Given that the slope of the line is 3, we can use the formula for average rate of change: (change in y) / (change in x). In this case, the change in x is 1 - (-4) = 5, and the change in y is 3 * 5 = 15. Therefore, the average rate of change is 15 / 5 = 3.
Related Questions
Is the number of fish caught during a fishing tournamentnumber of fish caught during a fishing tournament discrete or continuous?
Answers
The number of fish caught in a fishing tournament is a discrete variable, as it can only take specific or separate values which are whole numbers, not fractions or decimals.
Explanation:The number of fish caught during a fishing tournament would be considered a discrete variable in mathematics. This is because discrete variables are variables that can only take specific or separate values.
In this case, you can't catch half a fish or 2.3 fish in a tournament, you can only catch whole fish. This makes the number of fish caught a discrete variable because the count can only be in whole numbers. This is different from a continuous variable, such as the amount of time spent fishing or the weight of the fish caught, which could take on any value within a given range.
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Write the function in vertex form, and identify its vertex. g(x) = 5x2 - 50x + 128
Answers
g(x) = 5x² - 50x + 128
= 5(x²-10x +128/5)
= 5 (x²-10x+5²-5² +128/5)
= 5 ((x-5)² +128/5 -125/5)
y = 5 ((x-5)² - 3/5)
y= 5(x-5)² +3.....vertex form
the vertex is : (5,3)
In the triangle below, what is the side opposite the 30 degree angle
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A hypothesis is only tentative: to make sure it's valid, you have to ___________.
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School taxes for a local district are 2.5% of a households income if you ears 80,000 peryear how much do you pay in school taxes
Answers
Amount of income made by the Smith Household per year= $80000
Amount of money paid by the Smith's per year as school taxes = (2.5/100) * 80000
= 2.5 * 800
= 2000 dollars
So $2000 is the amount that the Smith's household needs to pay as school taxes every year. I hope the procedure needs no further clarification and the answer is what you were looking for.
Final answer:
To calculate school taxes for a household earning an annual income of $80,000 at a tax rate of 2.5%, multiply the income by the rate. The household would pay $2,000 in school taxes.
Explanation:
If a household earns an annual income of $80,000 and the school taxes are 2.5% of the income, the amount paid in school taxes can be calculated by multiplying the income by the tax rate. Here's the calculation:
Tax Amount = Income × Tax Rate
Tax Amount = $80,000 × 0.025
Tax Amount = $2,000
Therefore, a household that earns $80,000 per year would pay $2,000 in school taxes.
Jan is twice as old as her sister betty, but half of joe's age. betty just got married. how old is joe most likely to be?
Answers
x = 2y and x = 0.5z
Equating this two yields 2y = 0.5z. There are two variables but only one equation. Therefore, you have to specify one of the variables to be able to solve this problem. It was mentioned that Betty just got married. Let's assume that Betty's age was around 30 years old. Then, it follows that y=30. Substituting this to the final equation,
2(30) = 0.5z
z = 120 years old
This is impossible. Betty must have been married at an early age. Let's assume that Betty is 18 years old, then
2(18) = 0.5z
z = 72 years old
If Betty was 18 years old, then Joe is 72 years old. This is only an illustration to the problem. You must have introduced Betty's age to know the exact answer for Joe's age.
Mario and Luigi want to purchase some extra controllers for their friends.each controller costs 29.99. Use an algebraic expression to describe how much they spend in total,before sales tax,based on purchasing the console(299.00)the number of games(59.99 each) and the number of extra controllers
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Write the equation of a circle with center (-2,3) and a radius of 4. Show all work to receive credit.
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(x-a)^2+(y-b)^2=r^2
where:
(a,b) is the center of the circle
given that the center of our circle is (-2,3) with the radius of 4, the equation will be:
(x+2)^2+(y-3)^2=4^2
expanding the above we get:
x^2+4x+4+y^2-6y+9=16
this can be simplified to be:
x^2+4x+y^2-6y=16-13
x^2+y^2+4x-6y=3
The reciprocal is also called the _____.
a) multiplicative identity
b) multiplicative inverse
Answers
Answer:
multiplicative inverse
Step-by-step explanation:
hope it helps
Dr. Black is standing 15 feet from the streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 50°. To the nearest foot, the streetlamp is about _______
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the angle is from his shadow so use (15+8) as the adjacent side
so tan(50)=x/23
so tan(50)(23)=x
so x=about 27 feet
Find three positive numbers x, y, and z that satisfy the given conditions. the sum is 180 and the product is maximum.
Answers
(07.03 LC)
The steps below show the incomplete solution to find the value of p for the equation 4p − 2p + 4 = −1 + 21:
Step 1: 4p − 2p + 4 = −1 + 21
Step 2: 4p − 2p + 4 = 20
Step 3: 2p + 4 = 20
Which of these is most likely the next step?
2p = 5
2p = 8
2p = 16
2p = 24
Answers
First they combined like terms on one side.
Step 2: 4p − 2p + 4 = 20
Then they combined like terms on the other side.
Step 3: 2p + 4 = 20
Now you have to subtract 4 from both sides.
Step 4: 2p = 16
So the answer is C. 2p = 16
2p+4=20
-4=-4
2p = 16
how would you prove two circles are similar
Answers
GOOD LUCK!
Answer:
it is by similarity transformations
Step-by-step explanation:
so like it would be a rigid transformation then a dilation
EX- A translation then a dilation of R/r
What is the value of n in the equation –(2n + 4) + 6 = –9 + 4(2n + 1)?
Answers
Final answer:
The value of n in the equation –(2n + 4) + 6 = –9 + 4(2n + 1) is -2. This is determined by simplifying and solving the given expression for n.
Explanation:
To find the value of n in the equation –(2n + 4) + 6 = –9 + 4(2n + 1), we need to simplify and solve for n. First, we distribute the negative sign and the 4 into the parentheses and then combine like terms:
-2n - 4 + 6 = -9 + 8n + 4
Now, we combine the constants:
-2n + 2 = -5 + 8n
To isolate n, we move all the terms involving n to one side and the constants to the other:
-2n - 8n = -5 - 2
-10n = -7
Finally, we divide by -10 to solve for n:
n = ⅔
Thus, the value of n is -2.
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81
Answers
Honestly I believe this is correct:
∑ 15 at the top, n =0 (-9+6n)
the lines shown below are perpendicular. if the green line has a slope of 3/4, what is the slope of the red line
a)4/3
b)-3/4
c)-4/3
d) 3/4
Answers
the green line has a slope of 3/4
so the slope of the red line is -4/3
answer
c)-4/3
The slope of the red line is -4/3. Therefore, option C is the correct answer.
Given that, the green line has a slope of 3/4.
We need to find the slope of the red line.
What is the formula to find the slope of the perpendicular line?The formula for the slope of perpendicular lines is m1.m2 = -1. The product of the slopes of perpendicular lines is equal to -1.
Since, m1=3/4.
Now, 3/4.m2 = -1
⇒m2 =-4/3
The slope of the red line is -4/3. Therefore, option C is the correct answer.
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The volume of a cube is found using the formula l3, where l is the side length. What is the volume of a cube, in cubic feet that is 3/5 of a foot long
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If the telescope is 1 m deep and 8 m wide, how far is the focus from the vertex?
1
2
4
16
Find the vertex, focus, directrix, and focal width of the parabola.
negative 1 divided by 12 times x squared = y
Answers
(x-h)^2 = +/- 4a(y-k) or (y-k)^2=+/- 4a(x-h), where
(h,k) are the coordinates of the vertex
a is the distance of the vertex to the focus
4a = length of lactus rectum or the focal width
If the equation contains (x-h)^2, then the parabola passes the x-axis twice. Similarly, (y-k)^2 passes the y-axis twice. If the sign is (-), it opens to the left(if y-axis) or downward (if x-axis). If the sign is (+), it opens to the right(if y-axis) or upward (if x-axis).
The equation of the parabola is -1/12 x^2 = y. Rearranging to the general form:
x^2 = -12y
Therefore,
-4a = -12
4a = 12
a = 3, and the parabola is facing downwards.
The vertex is (0,0) at the origin.
The focus is (0,-3). Since it is negative, the focus is situated downwards, hence -3.
The directrix is the mirror image of the focus. Hence, it is a line passing +3 on the y-axis. y=3
Focal width is 4a which is equal to 12 units.
any ideas friends? cant seem to figure this out
Answers
Io = 10^(-12), which is a constant usually shown in a table or in your book
Plug in those values to get
B = 10*log(I/Io)
B = 10*log((7.6*10^(-4))/(10^(-12)))
B = 88.808135922808
B = 88.81
Answer: Approximately 88.81 decibels
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
Answers
A regular pyramid has a height of 12 centimeters and a square base. if the volume of the pyramid is 256 cubic centimeters, how many centimeters are in the length of one side of its base
Answers
The Volume of a pyramid is [tex] \frac{1}{3}*area_b_a_s_e *height[/tex]
the area of the base is a^2,
we apply the formula
[tex]256= \frac{1}{3}*a^{2}*12 [/tex]
[tex]256= 4a^{2} [/tex]
[tex]256= (2a)^{2} [/tex]
[tex]2a= \sqrt{256}=16[/tex]
a=8 (cm)
Answer: 8 cm
Simplify 15 to the 18th power over 15 to the 3rd power.
Answers
If the exponents you're dividing have the same base, you subtract them.
18 - 3 = 15
15^15
He sum of three consecutive odd integers is −375. find the three integers.
Answers
-375/3 = -125
-125-2 =-127
-125+2 = -123
-123 + -125 + -127 = -375
x+2 = second integer
x+4 = third integer
x + x+2 + x+4 = -375
3x = -375 - 6
3x = -381
x = -381/3 = -127 ← first integer
second integer = -127 + 2 = -125
third integer = -127 + 4 = -123
Answer: -127, -125 and -123
solve for y. 8x+y=15
Answers
y = 15 - 8x
8x = 15 + -1y
x = 1.875 + -0.125y
x = 1.875 + -0.125y
Super-yummy soup, inc. wants to paint their entire soup can red, including the top and bottom. if the diameter of the lid is 5 cm, and the height of the can is 9 cm, what is the approximate total surface area that will need to be painted?
Answers
The total surface area of the soup can would be equivalent to the sum of the surface area of the 2 covers plus the surface area of the side.
Surface area of the 2 covers = 2 π r^2
Surface area of the 2 covers = 2 π (2.5 cm)^2
Surface area of the 2 covers = 39.27 cm^2
Surface area of the side = 2 π r h
Surface area of the side = 2 π (2.5 cm) (9 cm)
Surface area of the side = 141.37 cm^2
Total surface area = 39.27 cm^2 + 141.37 cm^2
Total surface area = 180.64 cm^2
In physics, if a moving object has a starting position at s 0, an initial velocity of v 0, and a constant acceleration a, then the position S at any time t > 0 is given by:
S = at 2 + v 0 t + s 0.
Solve for the acceleration, a, in terms of the other variables. For this assessment item, you can use ^ to show exponents and type your answer in the answer box, or you may choose to write your answer on paper and upload it.
Answers
a=g
v=⌠g dt
v=gt+vi
s=⌠v
s=gt^2/2+vit+si
So if vi and si are zero then you just have:
s=gt^2/2
Notice that it is not gt^2 but (g/2) t^2
So the first term in any quadratic is half of the acceleration times time squared because of how the integration works out...
Anyway....
sf=(a/2)t^2+vit+si
(sf-si)-vit=a(t^2)/2
2(sf-si)-2vit=at^2
a=(2(sf-si)-2vit)/t^2 and if si and vi equal zero
a=(2s)/t^2
Step-by-step explanation:
The equation of a moving object in physics is given by :
[tex]s=at^2+v_ot+s_o[/tex]...........(1)
Where
s₀ is the starting position of an object
a is the acceleration of the object
v₀ is the initial velocity of the object
t is the time taken
We need to find the value of acceleration by rearranging equation (1). Subtract [tex](v_ot+s_o)[/tex] on both sides of equation (1) as :
[tex]s-v_ot-s_o=at^2[/tex]
Divide both sides of above equation by t² as :
[tex]a=\dfrac{s-v_ot-s_o}{t^2}[/tex]
So, the value of acceleration is [tex]\dfrac{s-v_ot-s_o}{t^2}[/tex]. Hence, this is the required solution.
Bruce had an EKG to measure his heartbeat rate. After conversion, the function produced could be modeled by a cosine function, and the wave produced a maximum of 4, minimum of −2, and period of pi over 2. Which of the following functions could represent Bruce's EKG read-out?
f(x) = 4 cos pi over 2x − 2
f(x) = 3 cos 4x + 1
f(x) = 3 cos pi over 2x + 1
f(x) = 4 cos 4x − 2
Answers
a = Amplitude = |4+2}/2 = |3|
Period = 2π/b = (2π) / (π/2) = 4
midline = (4-2)/2 = 1
Then the equation is:
y=3.cos(4x) + 1
Answer:
Option B.
Step-by-step explanation:
Bruce had an EKG to measure his heartbeat rate. After conversion, the function produced was modeled by a cosine function.
Now we will form this function.
Function will be in the form of f(x) = a cos(Bx) + d
Amplitude [tex]a=\frac{Maximum-minimum}{2}[/tex]
[tex]a=\frac{4+2}{2}=3[/tex]
Period = π/2
And [tex]Period=\frac{2\pi }{B}[/tex]
⇒[tex]\frac{\pi }{2}=\frac{2\pi }{B}[/tex]
⇒ B = 4
Since minimum is (-2) and maximum is (4), means cosine graph was shifted upwards.
Mid line of the graph is [tex]x=\frac{4+2}{2}=3[/tex] which shows graph is shifted by one unit above the x-axis.
Now the function we get is f(x) = 3 cos4x + 1
Therefore option B is the answer.
B is the midpoint of AC, D is the midpoint of CE. BD=10, and AE =2x. Find the length of CE if CD =3x
Answers
Since B is midpoint of AC and D is midpoint of CE, therefore, BD is parallel to AE and BD = 0.5 AE
AE = 2 BD = 2 x 10 = 2x
Therefore, x= 10
D is the midpoint of CE and CD = 3x, therefore CE = 6x where x = 10
Based on this, CE = 6 x 10 = 60 units of length
In how many ways can 50 cards be chosen from a standard deck of 52 cards?
Answers
The number of ways you can draw 50 cards from 52 is 52*51*50*49*48*47*...4*3 (it ends in 3).
,
But the number of ways that those 50 cards form the same set repeats is 50! = 50*49*49*47*....3*2*1
So, the answer is (52*51*50*49*48*....*3) / (50*49*48*...*3*2*1) = (52*51) / 2 = 1,326.
Note that you obtain that same result when you use the formula for combinations of 50 cards taken from a set of 52 cards:
C(52,50) = 52! / [(50)! (52-50)!] = (52*51*50!) / [50! * 2!] = (52*51) / (2) = 1,326.
Answer: 1,326
Simplify: 6/3-y -2/y